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How many different combinations are possible if a coin is tossed twice and a number cube is tossed once?
18 different combinations. When a coin is tossed twice there are four possible outcomes, (H,H), (H,T), (T,H) and (T,T) considering the order in which they appear (first or second). But if we are talking of combinations of the two individual events, then the order in which they come out is not considered. So for this case the number of combinations is three: (H,H), (H,T) and (T,T). For the case of tossing a die once there are six possible events. The number of different combinations when tossing a coin twice and a die once is: 3x6 = 18 different combinations.
How many possible combinations of 1 shirt and 1 pair of shorts can be made from 6 shirts and 3 pairs of shorts?
We select 1 shirt out of 6 shirts in (6 choose 1) ways or 6 ways. Then, we select 1 out of 3 pairs of shorts in (3 choose 1) or 3 ways. Therefore, the possible combinations of a shirt and a pair of shorts is 6 * 3 = 18 possible combinations.
What is the probability of rolling two 2's on two six-sided die?
The chance is 1/36. (There are 36 possible combinations for two 6-sided dice, but only 18 separate combinations when the dice are not considered seperately.)
What is the probability of rolling an odd number on 1 roll of die?
With a single die:There are 6 sides on a dice.There are 3 sides that are odd (1, 3, 5)3/6 = 1/2 = 50%Therefore, a single die has a 50% chance of landing on an odd number.If you have two dice:I'll explain this the longer way, however there are short (and simpler explanations) that basically use the fact that a single die is 50%, therefore two independent dice will also be 50%.Number of dice = 2Sides of a dice = 6Odd sides: 1, 3, 5, so Number of odd sides on a dice = 3Even sides: 2, 4, 6, so Number of even sides = 3Total combinations with two 6 sided dice = (sides on dice x sides on dice) = 6 x 6 = 36We need to take the fact that:An odd number + an odd number = evenAn even number + an even number = evenAn odd number + an even number = odd
A department store receives a shipment of 23 new portable radios There are 5 defective radios in the shipment If 4 radios are selected for display What is the probability that 2 of them are defective?
It is possible to choose 4 radios out of 23 in (23 choose 4)=8855 ways. The number of those combinations where there are exactly 2 indefective and 2 defective is: (18 (the number of those indefective) choose 2)*(5 (the number of defective radios) choose 2)=1530 divided by 8855=1530/8855=306/1771 which is 17.2784%.
