Question

4. If a coin and a die are thrown
simultaneously what is the probability
of getting a tail and an odd number?
*​

Answer 1

Answer:

1/4

Explanation:

What is the probability of getting an odd number and a tail when a die is rolled and a coin is tossed simultaneously?

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Let A be the event that the coin comes up tails.

Let B be the event that the die comes up odd numbered.

We can express the probability of both events happening, P(A,B) , as P(A,B)=P(A|B)P(B) , by the law of conditional probability.

Assuming that the coin and die are fair and independent, then P(A|B)=P(A) , by the definition of independence.

Thus, P(A,B)=P(A)P(B) .

The probability the coin is tails is P(A)=12 , because each side is equally like (i.e., coin is fair).

The probability the die come up odd is P(B)=12 , because the total set of outcomes, (1,2,3,4,5,6) has three such numbers and all outcomes are equally likely (i.e., die is fair).

As a result, P(A,B)=P(A)/P(B)=1/21/2=1/4 .