An unbiased coin is tossed five times. Find the probability of the given event. (Enter your answer to five decimal places.) The coin lands heads exactly once.

5/32

Step-by-step explanation:

Probability is the ratio of the number of possible outcomes to the number of total outcome.

Given that a coin has a head and a tail, it means that the total number of outcome is 2

Hence the probability of getting a head when the coin is tossed once

P(H) = 1/2,

Probability of getting a tail when the coin is tossed once

P(T) = 1/2

If the coin is tossed 5 times the probability that the head lands once

H or THTTT or TTHTT or TTTHT or H

= (1/2)^5 + (1/2)^5 + (1/2)^5 + (1/2)^5 + (1/2)^5

= 5/32

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.