Question

Suppose we roll one fair six-sided die, and flip six coins. what is the probability that the number of heads is equal to the number showing on the die?

Answer 1

The probability that the number of heads is equal to the number showing on the die is $\frac{21}{128}$ .

According to the question

we roll one fair six-sided die, and flip six coins

i.e

The Total Outcomes is the product of the sample spaces for the dice and the coins.  

sample spaces for the dice = 6

sample spaces for the coins = 2⁶

S = 6.2⁶

S = 384

Now, The  probability is

Therefore, the Favorable Outcomes

Consider the number of ways to get each total of heads from 1 to 6.

= 2⁶-1 (as TTT is excluded )

= 63

The probability that the number of heads is equal to the number showing on the die

As

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

Probability(Event) = Favorable Outcomes/Total Outcomes

By substituting the values in the formula

Probability(Event) = $\frac{63}{384}$

Probability(Event) = $\frac{21}{128}$

Hence, the probability that the number of heads is equal to the number showing on the die is $\frac{21}{128}$

To know more about probability here:

brainly.com/question/11234923

#SPJ4