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.....
The person who goes to the cinema arrived home late.
My answer:
0.2*0.3=0.06
0.8*0.6=0.48
0.06+0.48=0.54
To calculate the probability that the person who goes to the cinema arrives home late, you need to consider the probabilities for both Kate and Claire. Let's break down the calculation step by step:
1. Probability that Kate goes to the cinema and arrives home late:
- The probability that Kate goes to the cinema is given as 0.2.
- The probability that Kate arrives home late, given that she goes to the cinema, is given as 0.3.
- To calculate the probability for this scenario, you multiply the two probabilities together: 0.2 * 0.3 = 0.06.
2. Probability that Claire goes to the cinema and arrives home late:
- The probability that Claire goes to the cinema is the complement of the probability that Kate goes, which is 1 - 0.2 = 0.8.
- The probability that Claire arrives home late, given that she goes to the cinema, is given as 0.6.
- To calculate the probability for this scenario, you multiply the two probabilities together: 0.8 * 0.6 = 0.48.
3. Probability that the person who goes to the cinema arrives home late:
- Since either Kate or Claire can go to the cinema, you need to consider the probabilities for both scenarios.
- In steps 1 and 2, you calculated the probabilities for each person going to the cinema and arriving home late: 0.06 and 0.48, respectively.
- To find the overall probability, you add these two probabilities together: 0.06 + 0.48 = 0.54.
Therefore, the probability that the person who goes to the cinema arrives home late is 0.54.