Answered

Solve your doubts and expand your knowledge with IDNLearn.com's extensive Q&A database. Discover the information you need quickly and easily with our reliable and thorough Q&A platform.

The table gives a set of outcomes and their probabilities. Let A be the event "the outcome is less than 6". Let B be the event "the outcome is divisible by 3". Are A and B independent events? Outcome Probability 1 0.1 2 0.2 3 0.2 4 0.2 5 0.2 6 0.1 yes no

Sagot :

In order to have independent events, we need to verify the following formula:

[tex]P(A\cap B)=P(A)\cdot P(B)[/tex]

For event A, the outcomes that are less than 6 are 1, 2, 3, 4 and 5, so the probability of event A is:

[tex]\begin{gathered} P(A)=P(1)+P(2)+P(3)+P(4)+P(5) \\ P(A)=0.1+0.2+0.2+0.2+0.2 \\ P(A)=0.9 \end{gathered}[/tex]

For event B, the outcomes that are divisible by 3 are 3 and 6, so:

[tex]\begin{gathered} P(B)=P(3)+P(6) \\ P(B)=0.2+0.1 \\ P(B)=0.3 \end{gathered}[/tex]

The intersection of these events is only number 3, so:

[tex]P(A\cap B)=P(3)=0.2[/tex]

Verifying the formula, we have:

[tex]\begin{gathered} 0.2=0.9\cdot0.3 \\ 0.2=0.27 \end{gathered}[/tex]

The result is false, so the events are not independent, therefore the answer is NO.

We appreciate your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Thank you for visiting IDNLearn.com. We’re here to provide dependable answers, so visit us again soon.