Players in sports are said to have "hot streaks" and "cold streaks. "For example, a batter in baseball might be considered to be in a slump, or cold streak, if that player has made 10 outs in 10 consecutive at-bats. Suppose that a hitter successfully reaches base \( 27 \% \) of the time he comes to the plate. Complete parts (a) through (d) below. (a) Find the probability that the hitter makes 10 outs in 10 consecutive at-bats, assuming at-bats are independent events. Hint: The hitter makes an out \( 73 \% \) of the time, P(hitter makes 10 consecutive outs) \( =\square \) (Round to five decimal places as needed.)

To find the probability that a hitter makes 10 outs in 10 consecutive at-bats, we'll use the given probability that the hitter makes an out \( 73\% \) of the time. The formula for independent events states that you multiply the probabilities together. Therefore, the probability of making an out in one at-bat is \( 0.73 \). For 10 consecutive at-bats, the calculation is: \[ P(hitter makes 10 consecutive outs) = (0.73)^{10} \] Calculating \( (0.73)^{10} \): \[ P(hitter makes 10 consecutive outs) \approx 0.01857 \] Rounding to five decimal places, we get: \[ P(hitter makes 10 consecutive outs) \approx 0.01857 \] So, the answer to your problem is \( 0.01857 \).