Multiple choice

Four die are thrown simultaneously. The probability that $4$ and $3$ appear on two of the die given that $5$ and $6$ have appeared on other two die is?

  1. $1/6$
  2. $1/36$
  3. $12/151$

  4. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The condition is given that two specific dice show 5 and 6. We need the probability that the remaining two dice show 4 and 3. There are 36 total outcomes for the remaining two dice. The favorable outcomes are (4,3) and (3,4), which is 2/36 = 1/18. Since 1/18 is not listed, 'None of these' is correct.

AI explanation

If 5 and 6 have appeared on two dice, the remaining two dice are independent and can land on any number. The probability of getting a 4 on one specific die and a 3 on the other is 1/6 multiplied by 1/6, which equals 1/36. Since the two remaining dice can be assigned to 4 and 3 in 2 ways, the probability is 2 multiplied by 1/36, which is 1/18. Since 1/18 is not listed, the correct choice is None of these.

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