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Zorluk: OrtaCompound Probability

A game at a school carnival involves drawing two wooden blocks from a bag without looking. The bag initially contains 9 red blocks, 7 yellow blocks, and 5 blue blocks. If a player draws two blocks one after the other without replacing the first block, what is the probability that the first block drawn is blue and the second block drawn is yellow?

  1. 112\frac{1}{12}Cevap
  2. B
    563\frac{5}{63}
  3. C
    47\frac{4}{7}
  4. D
    1241\frac{12}{41}

Cevap

112\frac{1}{12}
The correct answer is found by multiplying the probability of the first event by the probability of the second event, accounting for the reduced total pool. The probability of drawing a blue block first is 521\frac{5}{21}. Because this block is not replaced, only 20 blocks remain in the bag. The probability of then drawing a yellow block is 720\frac{7}{20}. Multiplying these probabilities gives 521×720=35420\frac{5}{21} \times \frac{7}{20} = \frac{35}{420}, which simplifies to 112\frac{1}{12}.

Adım Adım Çözüm

1
Calculate the total number of blocks initially in the bag.
9 (red)+7 (yellow)+5 (blue)=21 total blocks9 \text{ (red)} + 7 \text{ (yellow)} + 5 \text{ (blue)} = 21 \text{ total blocks}
The denominator for the first probability requires the total count of all possible outcomes.
2
Determine the probability of the first event (drawing a blue block).
521\frac{5}{21}
There are 5 blue blocks out of the 21 total blocks.
3
Determine the probability of the second event (drawing a yellow block) given that a blue block was already removed.
720\frac{7}{20}
Because the first block was not replaced, there are now 21−1=2021 - 1 = 20 total blocks. There are still 7 yellow blocks in the bag.
4
Multiply the probabilities of the two dependent events and simplify.
521×720=35420=112\frac{5}{21} \times \frac{7}{20} = \frac{35}{420} = \frac{1}{12}
To find the compound probability of both events occurring in sequence, you must multiply their individual probabilities.

Anahtar Kavram

Dependent Compound Probability
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Konular

Compound Probability

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