Whilst shopping, the probability that Caroline buys fruit is 0.4. The probability that Caroline buys a CD is 0.6. Buying fruit and buying a CD are independent of each other. Work out the probability that she only buys fruit, only buys a CD, or buys both.

buys fruit = 40%

              buys CD = 60%

              buys both = 24%

Step-by-step explanation:

The probability of buying only fruit is given as 0.4.

Move the decimal 2 places to the right to convert it into a percent.

40%

The probability of buying only a CD is given as 0.6.

Move the decimal 2 places to the right to convert it into a percent.

60%

The probability of buying both is: fruit AND CD.

AND means "multiply".  0.4 x 0.6 = 0.24

Move the decimal 2 places to the right to convert it into a percent.

24%

step-by-step explanation:

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.