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Mathematics

1 answer:

neonofarm [45]3 years ago

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A probability experiment is conducted in which the sample space of the experiment is upper s equals { 1 comma 2 comma 3 comma 4

Softa [21]

You can think of this experiment as follows: you have to select a random number between 1 and 15, where each number is equally likely to appear.

Player A wins if 3,4,5 or 6 are picked.

Player B wind is 10,11 or 12 are picked.

Two events are said to be mutually exclusive if they cannot happen at the same time. So, in our metaphor, the question is: can we pick a particular number, so that both players win simultaneously?

The question is no, because if player A wins, we have picked 3,4,5 or 6, and player B wins with none of these numbers.

Similarly, if player B wins, we have picked 10, 11 or 12, and player A wins with none of these numbers.

So, the two events cannot occur simultaneously.

If you want to be more formal, since the events are subset of the sample space, two events are mutually exclusive if their intersection is the empty set, and this is the case:

$A \cap B = \{3,4,5,6\}\cap\{10,11,12\} = \emptyset$

8 0

3 years ago

A locker combination consists of two non-zero digits. The digits in a combination are not repeated and range from 2 through 9.

77julia77 [94]

Answer:

Answer choice B

Step-by-step explanation:

There are two possibilities; in the first, the first digit is below 5, in the second, it is above. The probability of the first possibility is 3/8, because there are 3 possible digits below 5 and 8 total digits. In this scenario, the chance of the second digit being below 5 is 2/7, because one of the digits is taken. In the other possibility, which has a chance of 5/8, the probability of choosing a number below 5 is 3/7, since all of them are still available. Doing the arithmetic, you find that the total probability is 2/7. Hope this helps!

4 0

3 years ago

What is 04.151515... into a fraction

Sergio039 [100]

Answer:

$\displaystyle 4.\overline{15} = \frac{137}{33}$ .

Step-by-step explanation:

Start by separating this decimal number into its integer part and its fraction part:

$4.151515\cdots = 4 + 0.151515\cdots$

The most challenging task here is to express $0.151515\cdots$ as a proper fraction. Once that fraction is found, expressing the original number $4.151515\cdots$ will be as simple as rewriting a mixed number as an improper fraction.

Let $x = 0.151515\cdots$ . $(x + 4)$ would then represent the original number.

Note that the repeating digits appear in groups of two. Therefore, if the digits in $x$ are shifted to the left by two places, the repeating part will continue to match:

$\begin{aligned}x = 0.&151515\cdots && \\ 100\, x = 15.& 151515\cdots \end{aligned}$ .

Note, that this "shifting" is as simple as multiplying the initial number by $100$ (same as $10$ raised to the power of the number of digits that needs to be shifted.)