Part (A). rolling two six sided dices and observing the number of dots facing up

Question

Part (A). rolling two six sided dices and observing the number of dots facing up. find the following probabilities:

1- The probability of observing an even number on the first die given that the 2nd die is showing an odd number.

2-The probability that the 2nd die is showing an even number given that the first die is showing an odd number.

Part(B)- Roll a die, find the following probabilites:

1- The probability of observing a number greater or equal to 4 given that the die is showing an even number facing up.

2-The probability of observing a 3 given that the die is showing a number less than 5.

Please solve Part (A )and Part(B).

Explanation / Answer

Part (A)

1. The roll of the two dice are independent.

Therefore, the probability of observing an even number on the first die given that the 2nd die is showing an odd number = The probability of observing an even number on the first die = 3/6 = 0.5.

2. Again, the roll of the two dice are independent.

The probability that the 2nd die is showing an even number given that the first die is showing an odd number = The probability that the 2nd die is showing an even number = 3/6 = 0.5.

Part(B)

1. If the die is showing an even number, the possibilities are 2,4,6. 4 and 6 are greater than or equal to 4.

The probability of observing a number greater or equal to 4 given that the die is showing an even number facing up = 2/3 = 0.67.

2. If the die is showing a number less than 5, the possibilities are 1,2,3,4.

The probability of observing a 3 given that the die is showing a number less than 5 = 1/4 = 0.25.

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