Lucy and Zaki each throw a ball at a target. 0.4 0.6 Lucy's throw Hit Miss 0.2 0.8 0.2 0.8 Zaki's throw Hit Miss Hit Miss What is the probability that both Lucy and Zaki hit the target?

Mathematics Questions

Lucy and Zaki each throw a ball at a target. 0.4 0.6 Lucy’s throw Hit Miss 0.2 0.8 0.2 0.8 Zaki’s throw Hit Miss Hit Miss What is the probability that both Lucy and Zaki hit the target?

Short Answer

To find the probability of Lucy and Zaki both hitting the target, we first identify their individual success rates: Lucy has a 40% chance and Zaki has a 20% chance. Since these events are independent, we multiply their probabilities (0.4 * 0.2) to get a combined probability of 8%.

Step-by-Step Solution

Step 1: Identify Individual Probabilities

To calculate the combined probability of Lucy and Zaki hitting the target, we first need their individual probabilities of success. For Lucy, the probability of hitting the target is 0.4, while for Zaki, it is 0.2. These values represent the likelihood that each person will succeed in their attempt.

Step 2: Utilize Probability of Independent Events

The probabilities of Lucy’s and Zaki’s attempts hitting the target are considered independent events. This means that the outcome of one does not affect the other. To find the probability of both events occurring simultaneously, we will use multiplication.

Step 3: Calculate the Combined Probability

Now, multiply the individual probabilities of Lucy and Zaki hitting the target. This is done by performing the calculation: 0.4 (Lucy) * 0.2 (Zaki). The result is 0.08, which equates to 8%. Thus, the probability that both will hit the target is 8%.

What is the probability that both Lucy and Zaki hit …