The probability that Kate goes to the cinema is 0.2. If Kate does not go Claire goes. If Kate goes to the cinema the probability that she is late home is 0.3. If Clair goes to the cinema the probability that she is late home is 0.6.
Calculate the probability that
1. Kate goes to the cinema and is not late
2. The person who goes to the cinema arrives home late.
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
1. .2 * (1-.3) = ?
Either-or probabilities are found by adding the individual probabilities.
2. (.2 *3.) + (.8 *.3) = ?
To calculate the probabilities in this scenario, we need to use the principles of conditional probability. We will break down the problem into smaller steps to find the required probabilities.
1. Probability that Kate goes to the cinema and is not late:
To calculate this probability, we need to find the product of two probabilities: the probability that Kate goes to the cinema (0.2) and the probability that she is not late, given that she goes to the cinema (1 - 0.3 = 0.7).
Therefore, the probability that Kate goes to the cinema and is not late is 0.2 * 0.7 = 0.14 (or 14%).
2. Probability that the person who goes to the cinema arrives home late:
To calculate this probability, we need to consider two possible scenarios: either Kate goes to the cinema and is late, or Claire goes to the cinema and is late. We need to calculate the probability of each scenario and add them together.
The probability that Kate goes to the cinema and is late:
This is the product of two probabilities: the probability that Kate goes to the cinema (0.2) and the probability that she is late, given that she goes to the cinema (0.3).
So, the probability that Kate goes to the cinema and is late is 0.2 * 0.3 = 0.06 (or 6%).
The probability that Claire goes to the cinema and is late:
This is the product of two probabilities: the probability that Claire goes to the cinema (0.8, calculated as 1 - 0.2 since Kate does not go) and the probability that she is late, given that she goes to the cinema (0.6).
So, the probability that Claire goes to the cinema and is late is 0.8 * 0.6 = 0.48 (or 48%).
To find the probability that the person who goes to the cinema arrives home late, we add together the probabilities from each scenario:
0.06 + 0.48 = 0.54 (or 54%).
Therefore, the probability that the person who goes to the cinema arrives home late is 0.54 (or 54%).