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What does equally unlikely mean in probability?
Two events are equally unlikely if the probability that they do not happen is the same for each event. And, since the probability of an event happening and not happening must add to 1, equally unlikely events are also equally likely,
What is the probability of flipping heads and rolling an odd number?
These would be independent events; therefore, we can multiply the probabilities of each of the two events. Probability of flipping a head: 1/2 Probability of rolling an odd number with a single die: 1/6 Required probability : 1/2 x 1/6 = 1/12
A sample space consists of 10 separate events that are equally. what is the probability of each?
I believe you mean to say, equally probable. By stating they are separate events, I assume that they are independent and that there is a single unique outcome to each event that can be identified. Ok, then the chance of each event or outcome is 1/10.
If you toss a coin 3 times what is the probability that it will land on heads 3 times?
The probability of getting heads on three tosses of a coin is 0.125. Each head has a probability of 0.5. Since the events are sequentially unrelated, simply raise 0.5 to the power of the number of tosses (3) and get 0.125, or 1 in 8.
How can you state and illustrate the addition multiplication Theorem of Probability?
Addition Theorem The addition rule is a result used to determine the probability that event A or event B occurs or both occur. ; The result is often written as follows, using set notation: : ; where: : P(A) = probability that event A occurs : P(B) = probability that event B occurs : = probability that event A or event B occurs : = probability that event A and event B both occur ; For mutually exclusive events, that is events which cannot occur together: : = 0 ; The addition rule therefore reduces to : = P(A) + P(B) ; For independent events, that is events which have no influence on each other: : ; The addition rule therefore reduces to : ; Example ; Suppose we wish to find the probability of drawing either a king or a spade in a single draw from a pack of 52 playing cards. ; We define the events A = 'draw a king' and B = 'draw a spade' ; Since there are 4 kings in the pack and 13 spades, but 1 card is both a king and a spade, we have: : = 4/52 + 13/52 - 1/52 = 16/52 ; So, the probability of drawing either a king or a spade is 16/52 (= 4/13).MultiplicationTheorem The multiplication rule is a result used to determine the probability that two events, A and B, both occur. The multiplication rule follows from the definition of conditional probability. ; The result is often written as follows, using set notation: : ; where: : P(A) = probability that event A occurs : P(B) = probability that event B occurs : = probability that event A and event B occur : P(A | B) = the conditional probability that event A occurs given that event B has occurred already : P(B | A) = the conditional probability that event B occurs given that event A has occurred already ; For independent events, that is events which have no influence on one another, the rule simplifies to: : ; That is, the probability of the joint events A and B is equal to the product of the individual probabilities for the two events.
