11. three cards are dealt from a well-shuffled deck. (a) find the chance that all of the cards are diamonds. (b) find the chance that none of the cards are diamonds. (c) find the chance that the cards are not all diamonds



Answer :

The chances of selected card being diamond is 3/13. The chance of none of the card being diamond is 1/13 by the probability concept "the extent to which something is probable; the likelihood of something happening or being the case."

What is probability?

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution. The sample space, or individual space, of a random experiment is the entire set of outcomes that could possibly occur. Any event's probability of happening ranges from 0 to 1. Mathematics' study of random events is known as probability, and there are four main types of probability: axiomatic, classical, empirical, and subjective. Since probability is the same as possibility, you could say that it is the likelihood that a specific event will occur.

Here,

a. The chance that all of the cards are diamonds,

number of diamond cards=13

=3/13

b. the chance that none of the cards are diamonds,

number of diamond card=13

total card=52

remaining card=52-13=39

=3/39

The probability that the chosen card is a diamond is 3/13. According to the definition of probability, which is "the degree to which something is probable; the likelihood of something happening or being the case," there is a 1/13 chance that none of the cards will be diamonds.

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