Question

s3 l3 5. calculate the probability of the event. you are tossing a weighted die. p(1)=0.30 chance of landing on the number 1. the die is rolled twice. what is the probability that the die will land on 1 twice?

Explanation:

Step1: Recall probability - multiplication rule for independent events

For independent events, if the probability of an event \(A\) occurring in one - trial is \(P(A)\) and the event is repeated \(n\) times, the probability of \(A\) occurring \(n\) times is \(P(A)\times P(A)\times\cdots\times P(A)=P(A)^n\). Here, the two rolls of the die are independent events, and the probability of getting a 1 in a single roll, \(P(1) = 0.30\).

Step2: Calculate the probability of getting 1 twice

We want to find the probability of getting 1 on the first roll and 1 on the second roll. Using the multiplication rule for independent events, the probability \(P\) that the die lands on 1 twice is \(P=P(1)\times P(1)\). Substitute \(P(1)=0.30\) into the formula: \(P = 0.30\times0.30=0.09\).

Answer:

0.09