Select the correct answer.
Rita is making a beaded bracelet. She has a collection of 160 blue beads, 80 gray beads, and 240 pink beads. What is the estimated probability that Rita will need to pick at least five beads before she picks a gray bead from her collection?
Use the table of randomly generated outcomes to answer the question. Each letter represents the first letter of the bead color.
Outcomes
PBBB
GPBP
PBPP
GGGG
BPBP
GBPB
GPBP
GBPB
PBPP 
PPGP
PBGG
GPPB
PPPG
BPPP
PPPG
BPGP
GGGG
PGPG
PPPP
PPPP
BBBG
PPGB
BBBG
PPGB
PBPB 
BPPG
PBBG
BPBB
PGPP
PBPP
PPPP
PBPP
PPBP
PPBB
PGBP
BPPB
PPPB 
PPPB
PGGB
BBBB

 A. 
0.05
 B. 
0.10
 C. 
0.45
 D. 
0.55


To determine the estimated probability that Rita will need to pick at least five beads before she picks a gray bead, we need to analyze the given table of outcomes. Specifically, we are looking for sequences where the first gray bead appears at or after the fifth position.

Here is the list of outcomes provided:
PBBB, GPBP, PBPP, GGGG, BPBP, GBPB, GPBP, GBPB, PBPP, PPGP, PBGG, GPPB, PPPG, BPPP, PPPG, BPGP, GGGG, PGPG, PPPP, PPPP, BBBG, PPGB, BBBG, PPGB, PBPB, BPPG, PBBG, BPBB, PGPP, PBPP, PPPP, PBPP, PPBP, PPBB, PGBP, BPPB, PPPB, PPPB, PGGB, BBBB.

To estimate the probability, count the number of sequences in which the first gray bead (G) appears at the fifth position or later. If a sequence has no gray beads in the first four positions, it is included.

Let's examine each sequence:
- PBBB: No gray bead in the first four positions.
- GPBP: Gray bead in the first position.
- PBPP: No gray bead in the first four positions.
- GGGG: Gray bead in the first position.
- BPBP: No gray bead in the first four positions.
- GBPB: Gray bead in the first position.
- GPBP: Gray bead in the first position.
- GBPB: Gray bead in the first position.
- PBPP: No gray bead in the first four positions.
- PPGP: No gray bead in the first four positions.
- PBGG: No gray bead in the first four positions.
- GPPB: Gray bead in the first position.
- PPPG: No gray bead in the first four positions.
- BPPP: No gray bead in the first four positions.
- PPPG: No gray bead in the first four positions.
- BPGP: No gray bead in the first four positions.
- GGGG: Gray bead in the first position.
- PGPG: No gray bead in the first four positions.
- PPPP: No gray bead in the first four positions.
- PPPP: No gray bead in the first four positions.
- BBBG: No gray bead in the first four positions.
- PPGB: No gray bead in the first four positions.
- BBBG: No gray bead in the first four positions.
- PPGB: No gray bead in the first four positions.
- PBPB: No gray bead in the first four positions.
- BPPG: No gray bead in the first four positions.
- PBBG: No gray bead in the first four positions.
- BPBB: No gray bead in the first four positions.
- PGPP: No gray bead in the first four positions.
- PBPP: No gray bead in the first four positions.
- PPPP: No gray bead in the first four positions.
- PBPP: No gray bead in the first four positions.
- PPBP: No gray bead in the first four positions.
- PPBB: No gray bead in the first four positions.
- PGBP: No gray bead in the first four positions.
- BPPB: No gray bead in the first four positions.
- PPPB: No gray bead in the first four positions.
- PPPB: No gray bead in the first four positions.
- PGGB: No gray bead in the first four positions.
- BBBB: No gray bead in the first four positions.

Count the number of sequences with no gray bead in the first four positions:
- PBBB, PBPP, BPBP, PBPP, PPGP, PBGG, PPPG, BPPP, PPPG, BPGP, PGPG, PPPP, PPPP, BBBG, PPGB, BBBG, PPGB, PBPB, BPPG, PBBG, BPBB, PGPP, PBPP, PPPP, PBPP, PPBP, PPBB, PGBP, BPPB, PPPB, PPPB, PGGB, BBBB.

There are 33 sequences that fit the criteria.

Since there are 40 outcomes total:
Probability = Number of favorable outcomes / Total number of outcomes
Probability = 33 / 40 = 0.825

None of the provided answers directly match this probability. However, reviewing the potential answer choices:

A. 0.05
B. 0.10
C. 0.45
D. 0.55

None of these answers are close to 0.825. There might be a discrepancy or an error in the problem statement or answer choices. Based on the analysis provided, the correct estimated probability should be approximately 0.825, but none of the provided answers match this.

Learn how to estimate the probability of picking at least five beads before picking a gray bead from a collection of beads. This problem involves analyzing outcomes and counting favorable sequences based on specified conditions.

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