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MMLU-Pro / 8650 / Bowl B₁ contains two white chips, bowl B₂ contains two red chips, bowl…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

Bowl B1B_1 contains two white chips, bowl B2B_2 contains two red chips, bowl B3B_3 contains two white and two red chips, and bowl B4B_4 contains three white chips and one red chip. The probabilities of selecting bowl B1,B2,B3B_1, B_2, B_3, or B4B_4 are 1/2,1/4,1/81 / 2,1 / 4,1 / 8, and 1/81 / 8, respectively. A bowl is selected using these probabilities and a chip is then drawn at random. Find P(W)P(W), the probability of drawing a white chip.
Plain-text mathematical notation (without MathML)
Bowl B₁ contains two white chips, bowl B₂ contains two red chips, bowl B₃ contains two white and two red chips, and bowl B₄ contains three white chips and one red chip. The probabilities of selecting bowl B₁,B₂,B₃, or B₄ are 1/2,1/4,1/8, and 1/8, respectively. A bowl is selected using these probabilities and a chip is then drawn at random. Find P(W), the probability of drawing a white chip.
Original LaTeX notation
Bowl $B_1$ contains two white chips, bowl $B_2$ contains two red chips, bowl $B_3$ contains two white and two red chips, and bowl $B_4$ contains three white chips and one red chip. The probabilities of selecting bowl $B_1, B_2, B_3$, or $B_4$ are $1 / 2,1 / 4,1 / 8$, and $1 / 8$, respectively. A bowl is selected using these probabilities and a chip is then drawn at random. Find $P(W)$, the probability of drawing a white chip.

category

math

options

  1. $\frac{19}{32}$
  2. $\frac{13}{32}$
  3. $\frac{29}{32}$
  4. $\frac{15}{32}$
  5. $\frac{27}{32}$
  6. $\frac{25}{32}$
  7. $\frac{23}{32}$
  8. $\frac{17}{32}$
  9. $\frac{31}{32}$
  10. $\frac{21}{32}$

src

scibench-stat

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Source and history

upstream_id / Original problem ID
8650
task_id
d2024bb9-0da4-58fc-b719-c786243ac2fd
task_key
default--test--8650
task_revision_id
1
config / split
default / test

Official source

initial import